Alternate interior and alternate exterior angles converse
Sophie Bono, Caroline Green, Lauren Goode, and Page Kemna
DEFINITIONS: Alternate Interior angles converse- If 2 lines are cut by a transversal, such that the pair of alternate interior angles is congruent, then the lines are parallel. This is used to prove that LINES ARE PARALLEL.
This is a picture of alternate INTERIOR angles. We need to prove that lines KO and LN are parallel. Well, using the interiror angles converse, we can see that the angles between KO and LN are alternate interior angles. They are the same measurments, and KO and LN is cut by a transversal, JM. Therefore, we can say the lines KO and LN are parallel.
Which picture shows alternate interior angles and which shows alternate exterior angles?
answers:
The first picture is alternate exterior because angles C and B are alt. ext. angles and angles A and D are alt. ext. angles.
The second picture is alternate interior because angles A and D are alt. int. angles and angles C and B are alt. int. angles.
Alternate interior and alternate exterior angles converse
Sophie Bono, Caroline Green, Lauren Goode, and Page KemnaDEFINITIONS: Alternate Interior angles converse- If 2 lines are cut by a transversal, such that the pair of alternate interior angles is congruent, then the lines are parallel. This is used to prove that LINES ARE PARALLEL.
This picture shows you what the alternate EXTERIOR angles are with colors. As you can see, the measurements for the blue anles are on the outside, and they are the same measurments. Same goes with the pink. As a result, Line KO is parallel to line LN. (JM is the transversal.)
This is a picture of alternate INTERIOR angles. We need to prove that lines KO and LN are parallel. Well, using the interiror angles converse, we can see that the angles between KO and LN are alternate interior angles. They are the same measurments, and KO and LN is cut by a transversal, JM. Therefore, we can say the lines KO and LN are parallel.
http://www.google.com/imgres?imgurl=http://www.wyzant.com/Help/Images/theorem_img5.gif&imgrefurl=http://www.wyzant.com/Help/Math/Geometry/Lines_and_Angles/Angle_Theorems.aspx&usg=__78xkBvBntKYK0VC-RKtukvW-d6U=&h=287&w=472&sz=7&hl=en&start=18&zoom=1&tbnid=oELe07NZOD_09M:&tbnh=105&tbnw=172&prev=/images%3Fq%3Dalternate%2Binterior%2Bangles%2Bconverse%26um%3D1%26hl%3Den%26safe%3Dactive%26sa%3DN%26biw%3D1003%26bih%3D433%26tbs%3Disch:10%2C590&um=1&itbs=1&ei=t6bLTLCdDZG2sAPly7D-Dg&biw=1003&bih=433&iact=rc&dur=387&oei=HMrKTOf8LcP88Aal98SHAQ&esq=7&page=3&ndsp=10&ved=1t:429,r:4,s:18&tx=98&ty=60
Which picture shows alternate interior angles and which shows alternate exterior angles?
answers:
The first picture is alternate exterior because angles C and B are alt. ext. angles and angles A and D are alt. ext. angles.
The second picture is alternate interior because angles A and D are alt. int. angles and angles C and B are alt. int. angles.
http://www.gltech.org/library/April_geometry/angles.html